Volume 22, Issue 6

In order to improve the efficiency and accuracy of thermal and moisture comfort prediction of underwear, a new prediction model is designed by using principal component analysis method to reduce the dimension of related variables and eliminate the multi-collinearity relationship between variables, and then inputting the converted variables into genetic algorithm (GA) and BP neural network. In order to avoid the problems of slow convergence speed and easy falling into local minimum of Back Propagation (BP) neural network, this paper adopted GA to optimize the weights and thresholds of BP neural network, and utilized MATLAB software to program, and established the prediction models of BP neural network and GA–BP neural network. To verify the superiority of the model, the predicted result of GA–BP, PCA–BP and BP are compared with GA–BP neural network. The results show that PCA could improve the accuracy and adaptability of GA–BP neural network for thermal and moisture comfort prediction. PCA–GA–BP model is obviously superior to GA–BP, PCA–BP, BP, SVM and K-means prediction models, which could accurately predict thermal and moisture comfort of underwear. The model has better accuracy prediction and simpler structure.

In this paper we focus our attention on the design of the feedback-based feed-forward controller asymptotically stabilizing the double-pendulum-type (D-P-T) crane system with the time-varying rope length in the desired end position of payload (the origin of the coordinate system). In principle, two cases are considered, in the first case, the sway angle of payload is uncontrolled and second case, when the sway angle of payload is controlled by an external force. Precise mathematical modeling in the framework of Lagrange formalism without the traditional neglect of the important structural parameters of the D-P-T crane system and numerical simulation in the Matlab environment indicate the substantial reduction of the transportation time to the desired end position.

In this paper, we investigate the blowup, as well as global existence, and uniqueness of mild solutions for the initial-boundary value problem to a class of fractional extended Fisher–Kolmogorov equations with a general nonlinear term. We establish a general framework to find the global mild solutions for fractional extended Fisher–Kolmogorov equations with general nonlinear function, which will provide an effective way to deal with such problems. The results obtained in this paper can be considered as a contribution to this nascent field.

We consider Lipschitz stability of zero solutions to the initial value problem of nonlinear ordinary differential equations with non-instantaneous impulses on ordered Banach spaces. Using Lyapunov function, Lipschitz stability of zero solutions to nonlinear ordinary differential equation with non-instantaneous impulses is obtained.

In this article, a mathematical model has been derived for studying the dynamics of malaria disease and the influence of awareness-based interventions, for control of the same, that depend on ‘level of awareness’. We have assumed the disease transmission rates from vector to human and from human to vector, as decreasing functions of ‘level of awareness’. The effect of insecticides for controlling the mosquito population is influenced by the level of awareness, modelled using a saturated term. Organizing any awareness campaign takes time. Therefore a time delay has been incorporated in the model. Some basic mathematical properties such as nonnegativity and boundedness of solutions, feasibility and stability of equilibria have been analysed. The basic reproduction number is derived which depends on media coverage. We found two equilibria of the model namely the disease-free and endemic equilibrium. Disease-free equilibrium is stable if basic reproduction number (ℛ 0 ) is less than unity (ℛ 0  < 1). Stability switches occur through Hopf bifurcation when time delay crosses a critical value. Numerical simulations confirm the main results. It has been established that awareness campaign in the form of using different control measures can lead to eradication of malaria.

The Heisenberg hierarchy and its Hamiltonian structure are derived respectively by virtue of the zero-curvature equation and the trace identity. With the help of the Lax matrix, we introduce an algebraic curve K n ${\mathcal{K}}_{n}$ of arithmetic genus n , from which we define meromorphic function ϕ and straighten out all of the flows associated with the Heisenberg hierarchy under the Abel–Jacobi coordinates. Finally, we achieve the explicit theta function representations of solutions for the whole Heisenberg hierarchy as a result of the asymptotic properties of ϕ .

Most of the problems in mathematical and engineering sciences can be studied in the context of nonlinear equations. In this paper, we develop a new family of iterative methods for the approximation of the zeros of mathematical models whose governing equations are nonlinear in nature. The proposed methods are based on decomposition technique due to Daftardar-Gejji and Jaffri [1]. The new family gives several iterative schemes as special cases. The convergence analysis of proposed methods is also presented. In order to determine the performance of newly developed methods, numerical as well as graphical analysis of four complex mathematical models from diverse fields of science and engineering are considered. We also consider some complex polynomials to visualize the roots through polynomiography in the context of proposed methods.

In this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

In this manuscript, we investigate the existence, uniqueness, Hyer-Ulam stability and controllability analysis for a fractional dynamic system on time scales. Mainly, this manuscript has three segments: In the first segment, we give the existence of solutions. The second segment is devoted to the study of stability analysis while in the last segment, we establish the controllability results. We use the Banach and nonlinear alternative Lery-Schauder–type fixed point theorem to establish these results. Also, we give some numerical examples for different time scales. Moreover, we give two applications to outline the effectiveness of these obtained results.

In this article, we proposed an efficient numerical technique for the solution of fractional-order (1 + 1) dimensional telegraph equation using the Laguerre wavelet collocation method. Some examples are illustrated to inspect the efficiency of the proposed technique and convergence analysis is discussed in terms of a theorem. Here, the fractional-order telegraph equation is converted into a system of algebraic equations using the properties of the Laguerre wavelet, and solutions obtained by the proposed scheme are more accurate and they are compared with the analytical solution and other method existed in the literature.

The main aim of this work is to investigate numerical solutions of the two different types of the fifth-order modified Kawahara equation namely bell-shaped soliton solutions and travelling wave solutions that occur thereby the different type of the Korteweg–de Vries equation. For this approach, we have used an effective and simple type of finite difference method namely Crank-Nicolson scheme for time integration and third-order modified cubic B-spline-based differential quadrature method for space integration. We preferred the third-order modified cubic B-splines to solve the fifth-order partial differential equation because of by using low energy, less algebraic process and produce better results than earlier works. To display the efficiency and accuracy of the present fresh approach famous test problems namely bell-shaped single soliton that has negative amplitude and travelling wave solutions that have the both of the positive and negative amplitudes are solved and the error norms L 2 and L ∞ are calculated and compared with earlier works. Comparison of the error norms show that present fresh approach obtained superior results than earlier works by using same parameters. At the same time, two lowest invariants of the test problems during the simulations are calculated and reported. Besides those, relative changes of invariants are computed and reported.

In this paper, we introduce an Caputo fractional high-order problem with a new boundary condition including two orders γ ∈ ( n 1 − 1 , n 1 ] $\gamma \in \left({n}_{1}-1,{n}_{1}\right]$ and η ∈ ( n 2 − 1 , n 2 ] $\eta \in \left({n}_{2}-1,{n}_{2}\right]$ for any n 1 , n 2 ∈ ℕ ${n}_{1},{n}_{2}\in \mathrm{&#x2115;}$ . We deals with existence and uniqueness of solutions for the problem. The approach is based on the Krasnoselskii’s fixed point theorem and contraction mapping principle. Moreover, we present several examples to show the clarification and effectiveness.